OFFSET
1,1
COMMENTS
4*Q^2 + 3 always has a prime divisor congruent to 1 modulo 6.
If we start with the empty product Q=1 then it is not necessary to specify the initial prime. - Jens Kruse Andersen, Jun 30 2014
REFERENCES
P. G. L. Dirichlet (1871): Vorlesungen uber Zahlentheorie. Braunschweig, Viewig, Supplement VI, 24 pages.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, page 13.
LINKS
Sean A. Irvine, Table of n, a(n) for n = 1..48
EXAMPLE
a(4)=487 is the smallest prime divisor of 4*Q*Q + 3 = 10812186007, congruent to 1 (mod 6), where Q = 7*199*7761799.
MATHEMATICA
a={7}; q=1;
For[n=2, n<=7, n++,
q=q*Last[a];
AppendTo[a, Min[Select[FactorInteger[4*q^2+3][[All, 1]], Mod[#, 6]==1 &]]];
];
a (* Robert Price, Jul 16 2015 *)
PROG
(PARI) Q=1; for(n=1, 11, f=factor(4*Q^2+3); for(i=1, #f~, p=f[i, 1]; if(p%6==1, break)); print1(p", "); Q*=p) \\ Jens Kruse Andersen, Jun 30 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Oct 09 2000
EXTENSIONS
More terms from Nick Hobson, Nov 14 2006
More terms from Sean A. Irvine, Oct 23 2014
STATUS
approved